Today we are going to conduct a practical session on how Gedmatch Oracle calculators work.
As you have seen, after entering your kit number and receiving the results in % format and a pie chart, you have a button called Oracle and Oracle 4 where you get an approximation of populations in combinations of 1, 2, 3 and 4 populations.
Oracle 1 Population of Eurogenes K15
Without going into deep math details, we will explain the calculation of an Oracle population.
For this, we will see what is a distance Euclidean and Manhattan, with respect to the populations of the Spreadsheet that the calculators offers next to the Oracle and Oracle 4 button.
In the capture you see that there are a series of populations with a percentage distribution of pesos per component K.
Given this, if we want to compare ourselves with these reference populations and see how close or far we are from each of them (distance), we can calculate the Euclidean distance (used by Gedmatch) or Manhattan for this purpose.
This formula calculates (used by Gedmatch) a distance by summing the difference between the percentage that it gave us in each of the 15 components and those of the reference population and then making the square of said difference, finally making the square root of the sum.
We can alternatively use the distance Manhattan would apply this formula (this is not used by Gedmatch). That tries to extract the sum of the absolute values of the difference between each component.
The result for each comparison between our result and the population of the Spreadsheet will give us a distance, being closer to 0 closer / greater similarity, and when further away from 0 smaller similarity.
If we apply it to the entire spreadsheet of the K15 we get 206 distances. If we order it from least to greatest, we already have our Oracle 1. Easy, right?
As you can see, basic mathematics can give us relatively interesting details of our DNA inheritance.
I attached an Excel to calculate at home your populations of K15. Distance values may vary by the precision of decimals.